The renewed interest in lunar exploration and the development of future lunar communication and navigation services highlight the need for a precise, stable, and interoperable geodetic and timing infrastructure on the Moon. NovaMoon, proposed as a scientific and navigation payload for ESA's Argonaut lander, is designed as a lunar-based local differential, geodetic, and timing station supporting both operational needs in the Moon's south polar region and a broad range of scientific investigations. The payload integrates a lunar laser retroreflector, a Very Long Baseline Interferometry transmitter, a receiver for navigation signals compatible with LunaNet standards, high-stability atomic clocks, and direct-to-Earth radio links – making it the first lunar station to co-locate multiple ranging, tracking, and timing techniques. NovaMoon will enable sub-metre to decimetre positioning, provide local differential corrections for lunar users, and ensure an accurate and stable realisation of position and time. Preliminary simulation studies show that this multi-technique dataset improves the lunar reference frame, orientation and ephemerides, and estimates of interior parameters like tidal response and core properties. NovaMoon will also provide the first long-duration physical realisation of a lunar time reference. Beyond its primary goals, it supports improved cartography, precise surface geolocation, and higher-resolution topography, contributing to safer landings and operations. It also enables new tests of fundamental physics, including constraints on relativity and possible deviations from classical gravity.

Violations of Lorentz invariance, a cornerstone of modern physics, are predicted by theories of quantum gravity and by extensions of general relativity involving new vector or tensor fields. In the weak-field limit, such a violation would primarily manifest as a nonzero value for the post-Newtonian parameter α_{1}, which is identically zero in general relativity. We present a new test of local Lorentz invariance by searching for this signature in the orbits of the LAGEOS and LAGEOS II satellites. By applying a phase sensitive detection technique to the mean argument of latitude, derived from about 30 years of satellite laser ranging data, we isolate the periodic signal potentially induced by a preferred reference frame aligned with the cosmic microwave background. Our analysis yields a new constraint |α_{1}|∼2×10^{-5}. This result improves upon the previous best limit from lunar laser ranging and provides the most stringent constraint to date on preferred-frame effects in Earth's gravity.

Strong theoretical arguments suggest that a breakdown of Lorentz Invariance could arise under some very particular conditions. From an experimental point of view, it is important to test the Local Lorentz Invariance with ever greater precision and in all contexts, regardless of the theoretical motivation for the possible violation. In this paper we discuss some aspects of the gravitational sector. Tests of Lorentz Invariance in the context of gravity are difficult and rare in the literature. Possible violations could arise from quantum physics applied to gravity or the presence of vector and tensor fields mediating the gravitational interaction together with the metric tensor of General Relativity. We present our results in the latter case. We analyzed the orbit of the LAGEOS and LAGEOS II satellites over a period of almost three decades. The effects of the possible preferred frame represented by the cosmic microwave background radiation on the mean argument of latitude of the satellites orbit were considered. These effects would manifest themselves mainly through the post-Newtonian parameter α_1, a parameter that has a null value in General Relativity. We constrain this parameterized post-Newtonian parameter down to the level of α_1 ≤ 2×10^-5, improving a previous limit obtained through the Lunar Laser Ranging technique.

The LAGEOS (LAser GEOdynamics Satellite) and LARES (LAser RElativity Satellite) geodetic satellites have been instrumental also in probing fundamental physics and testing gravitational theories in the weak-field and slow-motion limit of General Relativity (GR). This review paper summarizes key scientific challenges and achievements, focusing on the Precise Orbit Determination (POD) of these passive satellites, the accurate modeling of non-gravitational perturbations, and the subsequent use of orbital residuals to constrain post-Newtonian parameters and alternative theories of gravity. We detail the advanced modeling techniques for spin dynamics, neutral drag, and thermal thrust effects, crucial for achieving millimeter-level precision in orbit. The core of the analysis relies on excluding GR effects from the dynamical models during POD, thus preserving relativistic signatures in the orbital residuals. The paper highlights significant results from the LARASE and SaToR-G projects, including precise measurements of the Schwarzschild and Lense-Thirring precessions. These measurements have yielded stringent constraints on combinations of PPN parameters, non-symmetric gravitation theories, torsional theories, and Yukawa-like long-range interactions, considerably advancing our understanding of gravitational physics beyond GR’s predictions. Future directions include leveraging the mean anomaly as an additional observable and exploring violations of Local Lorentz Invariance to further refine these tests.

GUEST is a space mission concept whose central objective is the detection of gravitational waves (GWs) in the microhertz band – a physics-rich frequency window that no other present or planned detector can reach at a significant level. The concept is simple: two dense, passive spheres, covered with cube-corner retroreflectors, deployed in highly eccentric Earth orbits (e ≳ 0.7, period P ≳ 33 h), tracked continuously by the global network of satellite laser-ranging stations over a minimum observation time of 10 years, with an expected total duration of 30 years. The orbits themselves act as resonant detectors of the oscillating gravitational perturbations, with the microhertz sensitivity emerging from the selected orbital parameters. From the same data stream, GUEST delivers a programme of fundamental and applied science that cuts across particle physics, gravitational-wave astronomy, cosmology, astrophysics, and geodesy: the first coherent search for GWs from supermassive black-hole binaries in the μHz band, the exploration of primordial GW backgrounds in the unexplored energy-scale gap between pulsar-timing arrays and LISA, a dedicated probe of ultra-light dark matter in a parameter region untouched by any other experiment, a new way to search for ultra-light bosons, order-of-magnitude-improved tests of new gravitational interactions at astronomical ranges, and a step change in the absolute determination of GM_⊕ that underpins the Global Geodetic Observing System and future navigation and Earth-observation missions. This white paper presents the motivation, scientific reach, and mission concept of GUEST.

The Italian Spring Accelerometer (ISA) is a three axis mass-spring accelerometer, one of the payloads of the BepiColombo joint space mission between the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA). At launch in October 2018, BepiColombo started its seven-year cruise as a stack of three different modules, overall named Mercury Composite Spacecraft (MCS). The spacecraft will provide BepiColombo the necessary Delta V to reach Mercury with its electric thrusters and along with one, two and six gravity assists, respectively with Earth, Venus and Mercury. The accelerometer is accommodated on the Mercury Planetary Orbiter (MPO) module and, jointly with the Ka-band Transponder (KaT) tracking data, will primarily serve the BepiColombo Radio Science Experiment (BC-RSE). During the second Venus swing-by, strong tidal effect and external perturbations was expected to act on the spacecraft and to become detectable by ISA. The swing-by had a closest approach of about 550 km and the gravity gradient expected on the IDA sensing elements was perfectly measured. Hence, in this paper, the first direct Gravity Gradient effect detection generated by an extraterrestrial body is shown. Nevertheless, around the closest approach, the measurements evidenced a spurious acceleration event lasting for several minutes. This work, exploiting information on the Attitude and Orbit Control System (AOCS) commanded torques, focuses and analyses this ISA acceleration signal, ascribing it to a net force really acting on the MCS spacecraft. Furthermore, using an estimation method, the application point of the force is confined to an area close to the MPO radiator.

The Galileo for Science Project (G4S_2.0) is funded by the Italian Space Agency and has several goals in the field of Fundamental Physics to be achieved by exploiting the satellites of the Galileo-FOC Constellation. In this regard, a key point is to obtain a suitable satellite orbit solution by performing an accurate Precise Orbit Determination (POD). To this purpose modeling in a reliable way the complex effects of the Non-Conservative Forces, i.e. of Non-Gravitational Perturbations (NGPs), is essential. The activities undertaken in the construction of a Box-Wing model and of a Finite Element Model of the satellite will be presented with the preliminary results obtained by including these models into the POD of the Galileo satellites. In particular, using the orbital element residuals obtained from a POD we can test our new models and the improvements in POD quality.

The Galileo for Science Project (G4S_2.0) is funded by the Italian Space Agency and hasseveral goals in the field of Fundamental Physics to be achieved by exploiting the satellitesof the Galileo-FOC Constellation and the accuracy of their onboard atomic clocks. Inparticular, the clock-bias, estimated in the data reduction of the tracking observationsallows to place constraints on the possible presence of Dark Matter in our galaxy in theform of Domain Walls (DW) eventually produced in the very early Universe by ultralightscalar field(s). The impact of the DW on an atomic clock would provide a delta-liketransient shift on the pseudo-derivative of the clock-bias. Such signal depends both on thenature of the clock and the characteristics of the ultralight scalar comprising the DW.Ongoing work on the clock-bias will be introduced as regards to data pre-processing andsimulations on false alarm and detection efficiency.

The Galileo for Science Project (G4S_2.0) is an ongoing project funded by the Italian Space Agency that has several goals in the field of Fundamental Physics by exploiting the Galileo-FOC Constellation and, in particular, GSAT0201 (E18) and GSAT0202 (E14), the two satellite in elliptical orbit. By exploiting the accuracy of the atomic clocks on board the satellites, in particular of the clock-bias estimated in the process of data reduction of the tracking observations during a Precise Orbit Determination (POD), it allows on the one hand to measure the gravitational redshift, constraining the Local Position Invariance (LPI) and, on the other hand, to place constraints on the possible presence of dark matter in our galaxy in the form of Domain Walls. A fundamental point is obtaining a suitable satellite orbit solution by performing an accurate POD. In this context, the activities carried out with the Bernese code will be presented.

This paper introduces the main problems related to the modeling of the effects of nongravitational perturbations on satellites of the Galileo FOC constellation. The problem is addressed from the point of view of the scientific objectives of the Galileo for Science (G4S_2.0) project. These objectives are reflected in a set of fundamental physics measurements that will exploit the orbits and atomic clocks aboard the Galileo satellites, in particular the GSAT-0201 and GSAT-0202 satellites characterized by elliptical orbits, and not by almost circular orbits such as in the case of the remaining satellites of the constellation. The main focus is on the modeling of the direct solar radiation pressure, the largest nongravitational perturbation on GNSS satellites. After an in-depth presentation of the main nongravitational perturbations of interest, and of the models currently in use in the literature for their consideration, the work focuses on the amplitudes of the different effects and, with particular attention, on their intrinsic knowledge. Finally, two different models are introduced for the structure of the Galileo satellite specially developed for the objectives of G4S_2.0. The first is a simple model of the box-wing type, developed on the basis of the information currently available on the characteristics of the satellite. The second is a 3D model of the Galileo spacecraft, somewhat sophisticated due to the richness of the details on the structure and the various elements that make up the surfaces of the satellite. The activities carried out and in progress with these models and those planned with their subsequent updated versions are described.

This paper concerns the development of a first simplified model to take into account the perturbations produced by the nongravitational forces acting on the satellites of the Galileo FOC constellation and the corresponding first orbital determinations within the G4S_2.0 project. G4S_2.0 has a series of objectives in verifying the gravitational interaction in the weak field limit of the theory of general relativity, exploiting in particular the eccentricity of the orbits of some Galileo FOC satellites and the precise measurements that can be derived from the atomic clocks on board these satellites. The study focused on the model for the acceleration produced by direct solar radiation pressure on the satellites. This is the largest of all nongravitational perturbations. It is therefore necessary to build a sufficiently accurate model for it before being able to seriously consider smaller perturbation effects, such as those related to terrestrial radiation and thermal thrust effects. The work presents new aspects in the literature of navigation satellites. One of these is the determination of the effects in the Keplerian elements produced by the direct solar acceleration obtained from a box -wing model of the satellite. A second aspect is the comparison of these predictions in the orbital elements with the corresponding orbital residuals achieved from an orbit determination of the satellite. The study therefore highlights even more the importance of being able to improve the model of the perturbation originating from solar radiation in the field of global navigation satellite systems. This is very important if one wants to extract gravitational measurements from the orbit and clock -bias measurements of these satellites to verify the predictions of general relativity and compare them with those of alternative theories of gravitation.

ISA (Italian Spring Accelerometer) is a high sensitivity, relative, mass-spring accelerometer. It flies as scientific payload on-board the Mercury Planetary Orbiter (MPO), module of BepiColombo ESA mission to Mercury. The accelerometer is sensitive to any acceleration, greater than 2*10-8 ms-2Hz-1/2, that changes the spacecraft motion from a pure free fall: the, so called, Non Gravitational Perturbations (NGP). ISA data will be added, at Mercury, to the orbit determination estimation in order to help reconstructing the orbit and to make the MPO an a-posteriori free-fall satellite. After the first commissioning phase, performed in between November 2018 - August 2019, and that allowed to verify the functionality of the instrument itself, the first direct verification of the correct behaviour of the system was carried out during the BepiColombo Earth Flyby. Indeed, the spacecraft crossed the planet Earth shadow during the flyby and the direct Solar Radiation Pressure (SRP), the main contribution of NGP accelerations, dropped suddenly, marking a clear leap (gap) in the gathered data. The scientific team compared, on the base of the satellite surface exposition and radiative characteristics, the observed “drop” in the acceleration, once removed the on-board disturbances and inertial accelerations due to spacecraft rotations. In the talk, other ISA data recorded during the Earth Flyby are reported and expected signals for the upcoming Venus#2 Flyby and Mercury #1 Flyby are presented.

<p>The Galileo for Science Project (G4S_2.0) is an ongoing project funded by the Italian Space Agency that has several goals in the field of Fundamental Physics by exploiting the Galileo-FOC Constellation and, in particular, GSAT-0201 and GSAT-0202, the two FOC in elliptical orbit. The high eccentricity of their orbits and the accuracy of their atomic clocks allow to measure gravitational redshift and relativistic precessions of the orbits. These results will place new constraints on possible alternative theories of gravitation, both metric and non-metric in their structure. Furthermore, constraints on the presence of Dark Matter in our Galaxy can be placed by analysing data of the satellites’ atomic clocks.</p><p>In this framework a fundamental point is obtaining a suitable satellite orbit solution by performing an accurate Precise Orbit Determination (POD). To this purpose modeling, as better as possible, the complex effects of the Non-Gravitational Perturbations (NGPs) is essential. In particular, the direct Solar Radiation Pressure (SRP) represents the main source of error in determining the orbit of any GNSS spacecraft, as it is the largest NGPs perturbation.</p><p>Our final goal is to build a refined Finite Element Model (FEM) of the Galileo FOC spacecraft to compute the perturbing accelerations that will be used in the POD procedure.</p><p>As an intermediate step a Box-Wing (BW) model, as well as a 3D-CAD of the spacecraft, have been developed. We will present the results for the perturbing accelerations produced by SRP, Earth’s infrared radiation and Earth’s albedo in the case of a BW model built using the ESA Galileo metadata.</p><p>Moreover, accounting for multiple reflections and mutual shadowing effects is crucial to improve the POD and the scientific results. To this purpose we apply the so-called Ray Tracing technique to the spacecraft FEM. We will present our ongoing work on this technique by using the software COMSOL and Matlab on the current development we obtained for the FEM.</p><p>Finally, by using the residuals in the orbital elements obtained from a POD, we can test our new models and the improvements in the quality of the POD. In order to prove the reliability and robustness of the scientific results that will be obtained within G4S_2.0, we aim to exploit both GEODYN II and the Bernese software for the POD.</p>

We describe a proof-of-principle experiment aiming to investigate the inverse-square law of gravitation at the centimeter scale. The sensor is a two-stage torsion pendulum, while actuation is accomplished by a variable liquid mass. The time-varying gravitational force is related to the level of the circulating fluid in one or two containers at a short distance from the test mass, with all moving mechanical parts positioned at a large distance. We provide a description of the apparatus and present the first results. We identified a systematic effect of thermal origin, producing offsets of few fNm in torque and of about 10 pN in force. When this effect is neutralized, the measurements agree well with the predictions of simulations. We also discuss the upcoming instrument upgradations and the expected sensitivity improvement that will allow us to perform measurements with adequate accuracy to investigate the unexplored regions of the α-λ parameter space of a Yukawa-like deviation from the Newtonian potential.

<p>Within the G4S_2.0 (Galileo for Science) project, funded by the Italian Space Agency (ASI), two activities in the field of Fundamental Physics are under investigation and development: a new measure of the Gravitational Red Shift (GRS) and a search for possible Dark Matter (DM) candidates in the form of domain walls. Both researches are based on data from high-accuracy clocks aboard the satellites.</p><p>The GRS measurement exploits the two Galileo satellites DORESA and MILENA injected in 2014 into a wrong orbit characterized by a too high eccentricity. The corrected orbit, still has a relatively high eccentricity (about 0.16) suitable for gravitational measurements. Consequently, the clocks frequency of these two satellites is modulated with the changes of the Earth’s gravitational potential at the height of the satellite.</p><p>The search for DM matter is done by looking for the expected rapid perturbations in on-board clocks when a structure like a domain wall crosses Earth’s orbit and the Galileo constellation.  If this occurs, on-board clocks would have to change their frequency relative to a reference clock on Earth.</p><p>For both targets, a careful knowledge of the satellite’s position is required, to be obtained with a Precise Orbit Determination (POD) in which the main non gravitational perturbations, such as direct solar radiation pressure, are adequately modeled and accounted for. Furthermore, the clock data needs to be cleaned up by removing long-term drift and fast time jumps unrelated to the effects we want to measure.</p><p>We will present the preliminary results obtained within these activities.</p>

The G4S 2.0 project represents an important opportunity to perform fundamental physics measurements with the two Galileo-FOC satellites DORESA and MILENA in elliptic orbits. In this paper, we discuss the possibility to improve the current constraints on local position invariance via a new measurement of the gravitational redshift, taking into account both a new model of the satellites and more in-depth considerations on non-gravitational perturbations.

G4S_2.0 is a project funded by the Italian Space Agency aiming to perform a set of Fundamental Physics measurements using the two Galileo FOC satellites GSAT0201 (Doresa) and GSAT0202 (Milena). Indeed, the orbits of these satellites are characterized by a relatively high eccentricity, about 0.16, which represents a good prerequisite for a series of tests and measurements concerning the predictions of different theories of gravitation, as compared with the General Relativity (GR) ones. The main objectives include a new measurement of the gravitational redshift effect of the on-board atomic clocks --- thanks to its modulation with the orbital period due to the high eccentricity of the orbits --- and the measurement of the main precessions of relativistic origin, primarily the Schwarzschild one. To achieve these significant results, and possibly improve the current constraints of several theories of gravitation with respect to GR, it is of fundamental importance to take a step forward --- compared to the state of the art --- in the reliability of the dynamic model used for the orbits of the satellites and, as a direct consequence of this, in their precise orbit determination (POD). In this context, non-gravitational perturbations (NGPs) are the most subtle and difficult to model because of the complex shape of the Galileo satellites and their attitude law. In this regard, the main challenge is represented by a more refined and reliable model for the direct solar radiation pressure (SRP), the largest NGP on Galileo satellites, as well as on every satellite of every GNSS constellation. Our final goal is to build a finite element model (FEM) of the Galileo FOC spacecraft, as refined as possible, and apply a dedicated raytracing technique to it to compute the perturbing accelerations due to radiation pressure. In view of this, we have already developed a 3D-CAD model of the spacecraft. As an intermediate step, we have built a Box-Wing (BW) model based on the relatively poor information presently available on the geometrical and physical properties of the spacecraft. This BW model has been used to compute the perturbing accelerations due to the direct SRP and to the Earth's albedo and infrared radiation. The results obtained for the accelerations, to be included in the POD process, will be presented in various cases. Then, by computing the residuals in the orbital elements, it will be possible to verify the goodness of the POD results and observe the expected progressive improvement starting from the BW model towards the FEM one. The present analyses were made using the nominal attitude law of the Galileo FOC spacecraft; the application of this law will be discussed in the case of satellites in elliptical orbit. We finally highlight that the results of G4S_2.0 in terms of POD improvements are particularly useful for all applications of the Galileo FOC satellites in the fields of space Geodesy and Geophysics.

ISA (Italian Spring Accelerometer) is a scientific payload of the Mercury Planetary Orbiter (MPO) module of the ESA/JAXA BepiColombo mission to planet Mercury and it is the first high-sensitivity accelerometer on-board an interplanetary spacecraft. It will be one of the key instruments to perform Radio Science Experiments during the orbital phase. The instrument is sensitive to any acceleration, greater than 10-8 ms-2Hz-1/2, perturbing the free fall of the spacecraft in the overall gravity field. The main goal of ISA is indeed to measure the so-called Non Gravitational Perturbations (NGP) allowing to reconstruct, a posteriori, the motion of the spacecraft on a geodesic of spacetime. During the first Mercury flyby, performed in October 2021, the spacecraft approached the target planet reaching an altitude above its surface of only 200 km. Thanks to this very low altitude and to the ISA on-board position in cruise configuration, far away from the center of mass of the overall composite spacecraft, the accelerometer has been able to clearly detect the gravity gradient accelerations. Indeed, this is the first direct measurement of the gravity gradient acceleration induced on a spacecraft by the gravity field of a celestial object different from the Earth. Near the closest approach to the planet, the spacecraft entered in eclipse, losing the effect of the solar radiation pressure acting on its surfaces exposed to the Sun. As a consequence, a sudden change of the acceleration was clearly detected by the accelerometer; the measured signal has a magnitude aligned with the expectations, computed considering optical coefficients and spacecraft attitude. In June 2022, BepiColombo will carry out a second flyby that will be very similar, in terms of altitude, attitude and B-plane coordinates, to the first one, representing an almost unique opportunity to compare two similar measurements.